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The statement that quantity f(x) depending on x "can be made" arbitrarily large, corresponds to ∀y : ∃x : f(x) ≥ y. arbitrary A shorthand for the universal quantifier. An arbitrary choice is one which is made unrestrictedly, or alternatively, a statement holds of an arbitrary element of a set if it holds of any element of that set.
A domain is a set of all possible values that a variable is allowed to have. The values are ordered in a logical way and must be defined for each variable. Domains can be bigger or smaller. The smallest possible domains have those variables that can only have two values, also called binary (or dichotomous) variables.
the domain is the set of possible outcomes in a sample space (e.g. the set {,} which are the possible upper sides of a flipped coin heads or tails as the result from tossing a coin); and the range is a measurable space (e.g. corresponding to the domain above, the range might be the set { − 1 , 1 } {\displaystyle \{-1,1\}} if say heads H ...
A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, [5] are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.
As an example, given a set of people, we can consider the set of categorical variables corresponding to their last names. We can consider operations such as equivalence (whether two people have the same last name), set membership (whether a person has a name in a given list), counting (how many people have a given last name), or finding the ...
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
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Expected value or mean: the weighted average of the possible values, using their probabilities as their weights; or the continuous analog thereof. Median: the value such that the set of values less than the median, and the set greater than the median, each have probabilities no greater than one-half.